D-MAVT Design of integrated multi-energy systems with novel conversion technologies and seasonal storage

Transcription

1 Design of integrated multi-energy systems with novel conversion technologies and seasonal storage Paolo Gabrielli, Matteo Gazzani, Marco Mazzotti Separation Process Laboratory - Institute of Process Engineering

2 Motivation: from centralized energy generation Source: A. Gunzinger / Supercomputing Systems AG Paolo Gabrielli

3 to decentralized energy generation Source: A. Gunzinger / Supercomputing Systems AG Paolo Gabrielli

4 What is a multi-energy system (MES) electrical grid electricity MES: Conversion and Storage battery End Users PV panels PEMFC PtG PEME edhp solar radiation thermal solar H 2 HS gas-based conversion PEMFC SOFC MGT heat natural gas grid natural gas boiler TS Paolo Gabrielli

5 Main goal: design and analysis of MES with novel conversion technologies and seasonal storage Conversion technologies Seasonal storage Current approaches perform the design of integrated MES with a quite simplified description of the conversion technologies We want to provide more realistic models for such technologies within the design of MES Current approaches do not allow to consider the seasonal operation of complex multi-energy systems We want to enable the design and analysis of complex MES including seasonal storage with low computational complexity Paolo Gabrielli

6 Agenda 1. Modeling of fuel cell and electrolyzer devices a. Thermodynamic models b. Linear approximation methods 2. Formulation of the optimization problem a. Proposed methods for designing long-term storage systems b. Methods validation 3. Application of the proposed framework to design and analysis of integrated MES Paolo Gabrielli

7 Agenda 1. Modeling of fuel cell and electrolyzer devices a. Thermodynamic models b. Linear approximation methods 2. Formulation of the optimization problem a. Proposed methods for designing long-term storage systems b. Methods validation 3. Application of the proposed framework to design and analysis of integrated MES Paolo Gabrielli

8 Modeling electrochemical conversion devices MES: Conversion and Storage electrical grid electricity battery End Users PV panels PEMFC PtG PEME edhp solar radiation thermal solar H 2 HS gas-based conversion PEMFC SOFC MGT heat natural gas grid natural gas boiler TS Paolo Gabrielli

9 Electrochemical conversion devices: Fuel cells electricity heat electron flow fuel (e.g. H 2 ) oxidant (e.g. air) H + H 2 + O 2 H 2 O exhaust fuel (e.g. CO 2, H 2 ) anode electrolyte cathode Exhaust oxidant (e.g. air, H 2 O) PEM fuel cell, external methane reforming Fuel cells (FCs) are electrochemical devices that simultaneously generate electricity and heat through the electrochemical reaction of a fuel (e.g. H 2 or natural gas) with an oxidant (e.g. O 2 or air). Various types of FCs are considered: NG-SOFC, NG-PEMFC, H 2 -PEMFC Paolo Gabrielli

10 Electrochemical conversion devices: Electrolyzers electricity heat electron flow H2O H + H 2 O H 2 + O 2 O 2 anode electrolyte cathode H 2 PEM electrolyzer Electrolyzers are electrochemical devices that generate hydrogen and oxygen by absorbing electricity through the splitting of deionized water. High pressure PEM electrolyzers are considered, generating H 2 and O 2 at 40 bar. Paolo Gabrielli

11 Why first-principle models and how to use them P min A SOFC electrical power at different temperatures SOFC dynamic response to a variation in required thermal power Thermodynamic first-principle models are used to describe the nonlinear conversion performance and the dynamic features of the conversion technologies Computationally efficient approximations suitable for optimization framework Paolo Gabrielli

12 Modeling methodology CELL STACK Electrochemical model to describe cell performance MATLAB ENTIRE PRODUCT Energy and mass balances to describe the overall conversion performance ASPEN ENTIRE PRODUCT dynamic modeling to describe the overall transient behavior SIMULINK Paolo Gabrielli

13 Modeling methodology CELL STACK Electrochemical model to describe cell performance MATLAB ENTIRE PRODUCT Energy and mass balances to describe the overall conversion performance ASPEN ENTIRE PRODUCT dynamic modeling to describe the overall transient behavior SIMULINK P min A Paolo Gabrielli

14 Modeling methodology CELL STACK Electrochemical model to describe cell performance MATLAB ENTIRE PRODUCT Energy and mass balances to describe the overall conversion performance ASPEN ENTIRE PRODUCT dynamic modeling to describe the overall transient behavior SIMULINK Solid oxide fuel cell (SOFC) using natural gas and air Proton exchange membrane (PEM) fuel cell using natural gas and air PEM fuel cell using hydrogen and air PEM electrolyzer generating hydrogen and oxygen Power to gas Paolo Gabrielli

15 Linear approximation: conversion performance Steady-state behavior of conversion performance Conversion performance at reference conditions The thermodynamic model needs to be linearized to be used in an optimization framework Paolo Gabrielli

16 Linear approximation: conversion performance Steady-state behavior of conversion performance Conversion performance at reference conditions The thermodynamic model needs to be linearized to be used in an optimization framework Piecewise affine (PWA) approximation P α i F + β i S + γ i, i = 1,, N Paolo Gabrielli

17 Linear approximation: conversion performance Steady-state behavior of conversion performance Conversion performance at reference conditions The thermodynamic model needs to be linearized to be used in an optimization framework Piecewise affine (PWA) approximation P α i F + β i S + γ i, i = 1,, N Affine approximation P = αf + βs + γ Paolo Gabrielli

18 Linear approximation: dynamic behavior Dynamic behavior of the conversion performance Paolo Gabrielli

19 Linear approximation: dynamic behavior Dynamic behavior of the conversion performance First order approximation of the generated power: dq(t) dt = αq(t) + β Paolo Gabrielli

20 Linear approximation: dynamic behavior Dynamic behavior of the conversion performance First order approximation of the generated power: dq(t) dt = αq(t) + β Paolo Gabrielli

21 Linear approximation: dynamic behavior Dynamic behavior of the conversion performance First order approximation of the generated power: dq(t) dt = αq(t) + β Literature data: Start-up and shut-down times Ramp-up and ramp-down limitations In the form of constraints suitable for an optimization framework Paolo Gabrielli

22 Linear approximation: dynamic behavior Dynamic behavior of the conversion performance First order approximation of the generated power: dq(t) dt = αq(t) + β Literature data: Start-up and shut-down times Ramp-up and ramp-down limitations In the form of constraints suitable for an optimization framework Paolo Gabrielli

23 Agenda 1. Modeling of fuel cell and electrolyzer devices a. Thermodynamic models b. Linear approximation methods 2. Formulation of the optimization problem a. Proposed methods for designing long-term storage systems b. Methods validation 3. Application of the proposed framework to design and analysis of integrated MES Paolo Gabrielli

24 Optimal design of the multi-energy system electrical grid electricity MES: Conversion and Storage battery End Users PV panels PEMFC PtG PEME edhp solar radiation thermal solar H 2 HS gas-based conversion PEMFC SOFC MGT heat natural gas grid natural gas boiler TS Paolo Gabrielli

25 Optimization prob: mixed integer linear program min x,y c T x + d T y subject to Ax + By = b x 0, y {0, 1} electricity MES: Conversion and Storage battery End Users electrical grid edhp PV panels PEMFC PtG PEME solar radiation thermal solar H 2 HS gas-based conversion PEMFC SOFC MGT heat natural gas grid natural gas boiler TS Paolo Gabrielli

26 Optimization prob: mixed integer linear program min x,y decision variables c T x + d T y input data subject to Ax + By = b x 0, y {0, 1} objective function constraints electricity MES: Conversion and Storage battery End Users electrical grid edhp PV panels PEMFC PtG PEME solar radiation thermal solar H 2 HS gas-based conversion PEMFC SOFC MGT heat natural gas grid natural gas boiler TS Paolo Gabrielli

27 Optimal design problem: input data 1 Environmental conditions: solar irradiance and air temperature electricity MES: Conversion and Storage battery End Users electrical grid edhp PV panels PEMFC PtG PEME solar radiation thermal solar H 2 HS gas-based conversion PEMFC SOFC MGT heat natural gas grid natural gas boiler TS Paolo Gabrielli

28 Optimal design problem: input data 1 2 Environmental conditions: solar irradiance and air temperature Energy prices: electricity and gas prices MES: Conversion and Storage electricity battery End Users electrical grid edhp PV panels PEMFC PtG PEME solar radiation thermal solar H 2 HS gas-based conversion PEMFC SOFC MGT heat natural gas grid natural gas boiler TS Paolo Gabrielli

29 Optimal design problem: input data Environmental conditions: solar irradiance and air temperature Energy prices: electricity and gas prices Load demands: electricity and heat demands MES: Conversion and Storage electricity battery End Users electrical grid edhp PV panels PEMFC PtG PEME solar radiation thermal solar H 2 HS gas-based conversion PEMFC SOFC MGT heat natural gas grid natural gas boiler TS Paolo Gabrielli

30 Optimal design problem: input data Environmental conditions: solar irradiance and air temperature Energy prices: electricity and gas prices Load demands: electricity and heat demands Set of available technologies: cost and performance coefficients MES: Conversion and Storage electricity battery End Users electrical grid edhp PV panels PEMFC PtG PEME solar radiation thermal solar H 2 HS gas-based conversion PEMFC SOFC MGT heat natural gas grid natural gas boiler TS Paolo Gabrielli

31 Optimal design problem: input data Environmental conditions: solar irradiance and air temperature Energy prices: electricity and gas prices Load demands: electricity and heat demands Set of available technologies: cost and performance coefficients Assumptions Input data 1-3 are assumed to be known without uncertainty at every time instant t of the time horizon, based on past realizations. Therefore, the following hypotheses are implied: i. No evolution of input data occurs during following years ii. All the possible realizations of the uncertainty are included in historical data. Paolo Gabrielli

32 Optimal design problem: input data Paolo Gabrielli

33 Optimal design problem: decision variables I. Selection and size of the installed technologies II. Scheduling (ON/OFF status) of the conversion technologies III. Input and output power of the conversion technologies IV. Energy stored, charged/discharged by the storage technologies V. Imported/exported power from the grid PV panels thermal solar MES: Conversion and Storage PEMFC gas-based conversion PEMFC SOFC PtG H 2 PEME MGT HS edhp battery heat Operation variables II-V are determined at every hour of the year. boiler TS Paolo Gabrielli

34 Output power, P [kw] Optimal design problem: constraints I. Performance of conversion technologies: affine or piecewise affine (PWA) approximations P t = αf t + βsx t + γx t, t = F t min x t F t F t max x t, t = 1,, T 1,, T Original curve Binary variable x {0,1} T to model ON/OFF status. F min Affine approximation Input power, F [kw] F max Additional binary variables y, z {0,1} T to model start-up/shut-down dynamics. Paolo Gabrielli

35 Optimal design problem: constraints I. Performance of conversion technologies: affine or piecewise affine (PWA) approximations II. Performance of storage technologies: simple linear dynamics Input power, P Storage system Output power, P E t = E t 1 1 λδt + ηp t Δt, t = 1,, T E 0 = E T Stored energy, E 0 E t S, t = 1,, T S τ P t S τ, t = 1,, T Paolo Gabrielli

36 Optimal design problem: constraints I. Performance of conversion technologies: affine or piecewise affine (PWA) approximations II. Performance of storage technologies: simple linear dynamics III. Hub energy balances: the sum of imported and generated power must equal the sum of exported and used power Paolo Gabrielli

37 Optimal design problem: objective function I. Total annual cost of the system: I. Capital cost, modeled through a PWA function of the unit size II. Operation cost, function of the overall imported/exported energy along the year III. Maintenance cost, fraction of the capital cost II. Annual CO 2 emissions, function of the overall imported energy PV panels thermal solar MES: Conversion and Storage PEMFC gas-based conversion PEMFC SOFC PtG H 2 PEME MGT HS edhp battery heat The multi-objective optimization is performed through the ε-constraint method. boiler TS Paolo Gabrielli

38 Modeling challenge: time horizon The possibility of seasonal operation cycles translates in a long time horizon, with high resolution, which implies very large optimization problems Based on input data 1-3, the overall year is modeled through a set of D typical design days determined through a clustering procedure Traditionally, the design problem is solved for the design days, significantly reducing the computational complexity 01 Jan 02 Jan 31 Jan 01 Feb 02 Feb 28 Feb Typical design day I Typical design day II Typical design day III 01 Dec 31 Dec Paolo Gabrielli

39 Modeling the time horizon: novel methods Traditional method (M0) Typical input data Daily periodicity constraints Same stored energy for each design day Same stored energy variation at each design day Unit scheduling through design days Coupling design days (M1) Detailed input data (M2) Paolo Gabrielli

40 Modeling the time horizon: novel methods Traditional method (M0) Typical input data Daily periodicity constraints Same stored energy for each design day Same stored energy variation at each design day Unit scheduling through design days Coupling design days (M1) Typical input data Coupling constraints between different design days, using their sequence along the year Yearly periodicity constraints Free stored energy along the year Same stored energy variation at each design day Unit scheduling through design days Detailed input data (M2) Paolo Gabrielli

41 Modeling the time horizon: novel methods Traditional method (M0) Typical input data Daily periodicity constraints Same stored energy for each design day Same stored energy variation at each design day Unit scheduling through design days Coupling design days (M1) Typical input data Coupling constraints between different design days, using their sequence along the year Yearly periodicity constraints Free stored energy along the year Same stored energy variation at each design day Unit scheduling through design days Detailed input data (M2) Detailed input data Coupling constraints between different design days, using their sequence along the year Yearly periodicity constraints Free stored energy along the year Free stored energy variation along the year Unit scheduling through design days only for some technologies Paolo Gabrielli

42 Model validation: simple MES electrical grid electricity MES: Conversion and Storage battery End Users PV panels PEMFC PtG PEME solar radiation H 2 HS heat natural gas natural gas grid boiler Paolo Gabrielli

43 Model validation: computational time MIP gap = 0.01% The full scale optimization (FSO) requires about 23 hours to complete All the proposed methods require less than 1 hour for D = 3-72 Paolo Gabrielli

44 Model validation: long-term operation (D = 48) M0 determines a daily policy for storage operation, different for different design days M1 and M2 determine a longterm operation similar to that provided by the full scale optimization (FSO) Paolo Gabrielli

45 Model validation: system size M0 significantly underestimates the size of the storage system and overestimates the size of the conversion technologies, independently of the number of design days M1 and M2 provide a more accurate system design when increasing the number of design days (D > 25) Paolo Gabrielli

46 Model validation: total annual cost of the system Full scale optimizations featuring approximate system design: The design provided by M0 translates into significantly higher costs (~9%). The design provided by M1 and M2 translate into a lower cost (closer to the optimal value) when increasing the number of design days. M2 approaches the FSO value faster than M1 (~1% for D = 25-72). Paolo Gabrielli

47 Agenda 1. Modeling of fuel cell and electrolyzer devices a. Thermodynamic models b. Linear approximation methods 2. Formulation of the optimization problem a. Proposed methods for designing long-term storage systems b. Methods validation 3. Application of the proposed framework to design and analysis of integrated MES Paolo Gabrielli

48 Model application to a MES of interest electrical grid electricity MES: Conversion and Storage battery End Users PV panels PEMFC PtG PEME edhp solar radiation thermal solar H 2 HS gas-based conversion PEMFC SOFC MGT heat natural gas grid natural gas boiler TS Paolo Gabrielli

49 Cost-emission Pareto front The full scale optimizations did not complete in 5 days, whereas M2 with D = 48 was solved in less than 12 hours Tradeoff between capital and operational cost A reduction in both cost and emissions can be achieved with respect to a conventional scenario where electricity is bought from the grid and heat is generated with a boiler Paolo Gabrielli

50 Cost-emission Pareto front The reduction in both cost and emissions is mainly achieved through photovoltaic installation, replacement of boilers with heat pumps and utilization of thermal storage. Paolo Gabrielli

51 Sensitivity of Pareto fronts: solar installation Sensitivity analysis on the area available for solar installation: The level of minimum emissions depends on the amount of renewable energy installed All the Pareto sets coincide at low annual cost and then are separated at low emissions (high renewable and storage installations) Paolo Gabrielli

52 Sensitivity of Pareto fronts: solar installation Paolo Gabrielli

53 Sensitivity of Pareto fronts: solar installation Paolo Gabrielli

54 Take-home message We studied the optimal design of integrated MES including: Detailed description of electrochemical conversion technologies. Reduced order models were derived from first-principle models of fuel cells and electrolyzers and included within an optimization framework Seasonal operation cycles for the storage technologies. Two MILP approaches, based on design days, were proposed to enable the optimal design of complex MES including seasonal storage with limited computational complexity The optimal behavior of the system was investigated in terms of total annual cost and CO 2 emissions Seasonal operation cycles become convenient at low CO 2 emissions and are performed through power-to-gas technology, where hydrogen is generated through the excess of renewable energy Paolo Gabrielli

55 BACKUP SLIDES Paolo Gabrielli

56 Work in progress: tool development Paolo Gabrielli

57 Linear approximation: conversion performance Steady-state behavior of conversion performance Conversion performance at a reference temperature (neglecting temperature dependency at design phase) The thermodynamic model needs to be linearized to be used in an optimization framework Piecewise affine (PWA) approximation P α i F + β i S + γ i, i = 1,, N Paolo Gabrielli

58 Linear approximation: conversion performance Steady-state behavior of conversion performance Conversion performance at a reference temperature (neglecting temperature dependency at design phase) The thermodynamic model needs to be linearized to be used in an optimization framework Piecewise affine (PWA) approximation Linear approximation 1 Linear approximation 2 P α i F + β i S + γ i, i = 1,, N P = αf + βs + γ P = αf Paolo Gabrielli

59 Impact of modeling approximations: size Paolo Gabrielli

60 Impact of modeling approximations: cost Paolo Gabrielli

61 Modeling the time horizon: novel methods E t = λe t 1 + ηp t Δt, t = 1,, 8760 E 0 = E 8760 Methods Traditional method (M0): Typical demand profiles Daily periodicity constraint Same stored energy for each design day Unit commitment through design days Definition of D design days which are considered independently. E d,k = λe d,k 1 + ηp d,k Δk, d, k Description E d,0 = E d,k, d, k d = k = step 1,, D is the d-th design day 1,, K is the k-th daily time Paolo Gabrielli

62 Modeling the time horizon: novel methods E t = λe t 1 + ηp t Δt, t = 1,, 8760 E 0 = E 8760 Methods Traditional method (M0): Typical demand profiles Daily periodicity constraint Same stored energy for each design day Unit commitment through design days Method 1 (M1): Typical demand profiles Yearly periodicity constraint Free stored energy Unit commitment through design days Definition of D design days which are considered independently. Sequence of design days σ. Description E d,k = λe d,k 1 + ηp d,k Δk, d, k E d,0 = E d,k, d, k E y,k = λe y,k 1 + ηp σ(y),k Δk, y, k E y,1 = λe y 1,K + ηp σ(y),1 Δk, y d = 1,, D is the d-th design day E 0,K = E Y,K k = step 1,, K is the k-th daily time σ y D, y y = year 1,, Y is the y-th day of the Paolo Gabrielli

63 Modeling the time horizon: novel methods E t = λe t 1 + ηp t Δt, t = 1,, 8760 E 0 = E 8760 Methods Traditional method (M0): Typical demand profiles Daily periodicity constraint Same stored energy for each design day Unit commitment through design days Method 1 (M1): Typical demand profiles Yearly periodicity constraint Free stored energy Unit commitment through design days Method 2 (M2): Detailed demand profiles Yearly periodicity constraint Free stored energy variation Unit commitment through design days for some technologies Definition of D design days which are considered independently. Sequence of design days σ. Distinction between different decision variables. E d,k = λe d,k 1 + ηp d,k Δk, d, k E y,k = λe y,k 1 + ηp σ(y),k Δk, y, k E y,k = λe y,k 1 + ηp y,k Δk, y, k Description E d,0 = E d,k, d, k E y,1 = λe y 1,K + ηp σ(y),1 Δk, y E y,1 = λe y 1,K + ηp y,1 Δk, y d = 1,, D is the d-th design day E 0,K = E Y,K E 0,K = E Y,K k = step 1,, K is the k-th daily time σ y D, y y = year 1,, Y is the y-th day of the Paolo Gabrielli

64 Sensitivity of Pareto fronts: user demand Sensitivity analysis on ratio between thermal and electrical demands: The level of minimum emissions depends on the ratio between thermal and electrical demand Due to the possibility of efficiently converting electricity into heat (heat pumps), lower emissions can be achieved for high thermal-to-electrical demand ratio. Paolo Gabrielli

65 Sensitivity of Pareto fronts: user demand Paolo Gabrielli